transmission zeros to improve the selectivity in the similar fil-ter design.
ACKNOWLEDGMENTS
This work is supported by the Fundamental Research Funds for the Central Universities, the National Science Foundation of China under Grant 60801039, and the Guangdong Province Major science and technology project 2009A080207006.
REFERENCES
1. L.-C. Tsai and C.-W. Huse, Dual-band bandpass filter using equal-length coupled-serial-shunted lines and Z-transform techniques, IEEE Trans Microwave Theory Tech 52 (2004), 1111–1117. 2. H.-W. Deng, L. Zhao, and Y.-S. Kim, A dual-band BPF with
DSIR and TSIR, Elecron Lett 46 (2010), 1205–1206.
3. J. Wang, L. Ge, K. Wang, and W. Wu, Compact microstrip dual-mode dual-band bandpass filter with wide stopband, Elecron Lett 47 (2011), 263–265.
4. Q.-X. Chu and F.-Ch. Chen, A compact dual-band bandpass filter using meandering stepped impedance resonators, IEEE Microwave Wireless Compon Lett 18 (2008), 320–322.
5. H.-W. Deng, Y.-J. Zhao, X.-S. Zhang, W. Chen, and J.-K. Wang, Compact and high selectivity dual-band dual-mode microstrip BPF with single stepped-impedance resonator, Elecron Lett 47 (2011), 326–327.
6. M.A.S. Alkanhal, Dual-band bandpass filters using inverted stepped-impedance resonators, J Electromagn Waves Appl 23 (2009), 1211–1220.
7. C.H. Lee, I.C. Wang, and C.I.G. Hsu, Dual-band balanced BPF using k/4 stepped-impedance resonators and folded feed lines, J Electromagn Waves Appl 23 (2009), 2441–2449.
8. J.P. Wang, B.-Z. Wang, Y.X. Wang, and Y.-X. Guo, Dual-band microstrip stepped-impedance bandpass filter with defected ground structure, J Electromagn Waves Appl 22 (2008), 463–470. 9. Y.-C. Chang, C.-H. Kao, M.-H. Weng, and R.-Y. Yang, Design of
the compact dual-band bandpass filter with high isolation for GPS/ WLAN applications, IEEE Microwave Wireless Compon Lett 19 (2009), 780–782.
10. M.D.C. Velazquez-Ahumada, J. Martel-Villagr, F. Medina, and F. Mesa, Application of stub loaded folded stepped impedance reso-nators to dual band filter design, Prog Electromagn Res 102 (2010), 107–124.
11. J.-K. Xiao, S.-W. Ma, S. Zhang, and Y. Li, Novel compact split ring stepped-impedance resonator (SIR) bandpass filters with trans-mission zeros, Prog Electromagn Res 21 (2007), 329–339. 12. L. Guo, Z.-Y. Yu, and L. Zhang, Design of a dual-mode dual-band
filter using stepped impedance resonators, Prog Electromagn Res Lett 14 (2010), 147–154.
13. M.H. Weng, C.H. Kao, and Y.C. Chang, A compact dual-band bandpass filter with high band selectivity using cross-coupled asymmetric sirs for WLANs, J Electromagn Waves Appl 24 (2010), 161–168.
14. X. Lai, N. Wang, B. Wu, and C.-H. Liang, Design of dual-band fil-ter based on OLRR and DSIR, J Electromagn Waves Appl 24 (2010), 209–218.
15. X.-W. Dai, C.-H. Liang, G. Li, and Z.-X. Chen, Novel dual-mode dual-band bandpass filter using microstrip meander-loop resonators, J Electromagn Waves Appl 22 (2008), 573–580.
16. H.-J. Lin, X.Q. Chen, X.W. Shi, L. Chen, and C.L. Li, A dual passband filter using hybrid microstrip open loop resonators and coplanar waveguide slotline resonators, J Electromagn Waves Appl 24 (2010), 141–149.
17. S. Sun, and L. Zhu, Multiple-resonator-based bandpass filters, IEEE Microwave Mag 10 (2009), 88–98.
18. Z.-C. Hao and J.-S. Hong, Ultrawide band filter technologies, IEEE Microwave Mag 6 (2010), 56–68.
VC2012 Wiley Periodicals, Inc.
RECONFIGURING THE FREQUENCY
RESPONSE OF DISPERSIVE-CHANNEL
RADIO OVER FIBER SYSTEMS BY USING
FIBER PHOTONIC FILTERS: APPLICATION
TO TRANSMISSION OF MULTIPLEXED
MICROWAVE SUBCARRIERS
Celso Gutierrez-Martı´nez, Joel Santos-Aguilar, Misael Santiago-Bernal, Adolfo Morales-Dı´az, Jose Alfredo Torres-Fortiz, and Jacobo Meza-P erez Instituto Nacional de Astrofı´sica, Optica y Electronica (INAOE), Apdo Postal 51, 72000 Puebla, Pue. Mexico; Corresponding author: [email protected]
Received 12 October 2011
ABSTRACT:Radio over fiber schemes using multimode lasers and dispersive optical channel show a periodic band-pass microwave frequency response. Such a response can be used for implementing photonic microwave filters or for multiplexing modulated microwave subcarriers. The reconfiguration of the frequency response using optical retarders acting as photonic filters is demonstrated in this article. The multiplexed transmission of two data-modulated microwave subcarriers on two adjacent transmission windows is also described.VC2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 54:1869–1874, 2012; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.26972
Key words:multimode lasers; fiber optics dispersion; photonic filters; optical delays; radio over fiber; microwaves; electro-optic modulators
1. INTRODUCTION
Radio over fiber systems, using broadband optical sources and a dispersive optical media, can be potentially used either for imple-menting photonic microwave filters or for transmitting modulated microwave subcarriers for high-speed telecommunications.
The association of a dispersive propagation media and a multi-mode optical spectrum gives a periodic band-pass microwave response. A broadband optical spectrum can be realized using sets of tunable lasers (TLs), optically filtering the spectrum of er-bium-doped fiber amplifiers (EDFA), or using semiconductor multimode lasers diodes (MMLD). The dispersive media can be a standard single-mode optical fibers (SSMF), fiber Bragg gratings (FBG), or arrayed waveguide gratings. As an application of the association of a broadband optical spectrum and dispersive media, photonic microwave filters are being studied, aiming to show potential applications on radio over fiber systems and in high-speed signal processing [1–5]. The use of periodic band-pass response, for transmitting multiplexed microwave subcarriers, has been previously described [6, 7]. An important issue, related to the dispersive media-broadband optical source schemes, is the reconfiguration and tunability of the microwave frequency response. Many papers report on the tunability of the frequency response [7–14]. Most of these works are based on a set of TLs and either standard optical fibers [8] or fiber Brag gratings [9– 11], as the dispersive media. When using TLs and FBG, the schemes become relatively complex, as many TLs are required. Additionally other optical components as directional couplers, attenuators, power splitters, optical circulators, are necessary.
Simpler schemes, using a unique optical source, have been also proposed. Reconfiguration is obtained using a broadband amplified spontaneous emission from EDFA’s and delay lines [12]. In the work reported in Ref. 13, the reconfiguration is based on the shaping of the emission from an EDFA by a
dynamic gain equalizer; this shaping is followed by an optical filtering or slicing. A simple scheme describes the reconfigura-tion as based on varying the injecreconfigura-tion current on a multimode Fabry-Perot laser [14].
The work described in this article is as simple as the scheme in Ref. 14. However, in our case, the frequency response is reconfigured by filtering the optical spectrum as to increase the free spectral range (FSR). This approach is sim-pler to implement, as the optical spectrum can be modified by an optical retarder, acting as photonic filter. The photonic filter introduces an optical delay, or its equivalent optical path-dif-ference (OPD), which corresponds to a filtering function in the spectral domain [15, 16]. The photonic filter can be matched to the optical spectrum for achieving a selective elimination of optical modes thus increasing the FSR. In this way, the posi-tion and number of the band-pass transmission windows in the electrical frequency response can be reconfigured. In the first part of this article, we briefly recall the model of the frequency response of a radio over fiber scheme using a multimode laser and a dispersive optical fiber channel. The frequency response of a scheme associating a 0.5 nm FSR multimode laser and a 25 km dispersive optical fiber channel, shows band-pass micro-wave transmission windows centered at 0, 4, 8,…..GHz. This frequency response can be modified by OPD’s, which filter the optical spectrum and in this way, the electrical microwave response is reconfigured. When the 0.5 nm FSR optical spec-trum is filtered by an OPD of 2.2 mm, the FSR is increased to 1 nm and the frequency response will show transmission win-dows at 0, 2, 4, 6, 8,……GHz. If an OPD of 1.48 mm is used, the FSR is increased to 1.5 nm and the frequency response shows band-pass windows centered at 0, 1, 2, 3, 4,…….GHz. The filtering process is described and demonstrated.
In the second part of this article, as an illustrative potential application of the optical filtering process, we describe the ex-perimental multiplexed transmission of two data-modulated microwave subcarriers centered at 7 and 8 GHz, which result when an OPD of 1.48 mm has been used to filter the multimode laser spectrum. The multiplexed transmission-reception process is demonstrated, showing the self-filtering effect as given by the dispersive channel radio over fiber scheme. At the output of the optical receiver, the modulated subcarriers are detected by homodyne mixing and the base-band data is recuperated. No evaluation of the data transmission parameters (signal to noise ratio [SNR], bit error rate [BER], power penalty, etc.) is given as this aspect is beyond the scope of this article.
2. MICROWAVE BAND-PASS TRANSMISSION WINDOWS
Periodic band-pass microwave transmission windows, on radio over fiber schemes, result from the association of a multimode laser and a dispersive optical fiber channel. The frequency response of such a scheme is determined by the spectral charac-teristics of the optical source and by the length of the dispersive optical channel. The detailed model has been previously reported [6]. To recall the operating principle and the corresponding model, the basic scheme is presented in Figure 1. In the model, the optical source is represented by a complex random process sðtÞ ¼c tð ÞejXo twith optical spectrumP(X),Xis the optical
fre-quency. The transfer function of the optical channel is given as hfð Þ ¼t 21p
R1
1ejbð ÞXzejXtdX. To account for chromatic
disper-sion, the propagation constant can be expressed as
bð Þ ¼X b0 þb1ðXX0Þ þ12b2ðXX0Þ 2
.
As detailed elsewhere [6], if the light is intensity modulated by a signal mðtÞ ¼1þ4m0cosðxmtÞ, after transmission through
the optical channel of length z, the received average optical power is given as
P tð;xm;zÞ ¼
1 2p
Z
Pð ÞXdXþ2m0cos x2
m
2 b2z
cosðxmtþ xmb1zÞ Re
Z
PðXÞejðxmb2zðXX0ÞÞdX
(1)
As given by eq. (1), the optical power depends basically on the real part of the Fourier transform of the optical spectrum. If the optical source is a Gaussian-envelope, multimode laser diode, Figure 2(a), its optical spectrum is given as
PðXÞ ¼P0exp
4ðXX0Þ2
DX2
!
exp 4X
2
dX2
X1 n¼1
dðXndXÞ
" #
where X0 is the center optical frequency; DX is the envelope
optical bandwidth;dXis the FWHM of each optical mode and
dXis the FSR.
From Eq. (1), the frequency response of the multimode laser emission-dispersive optical channel, is proportional to
Pðxm;zÞaA0 exp DX xmb2z
4
2!
X1 1
d xmb2z
2pn
dX
" #
(2) The resulting frequency response shows a low-pass win-dow and series of band-pass winwin-dows, centered atfn ¼ DL@nk,
n is an integer.D is the fiber dispersion parameter, L is the optical fiber length.Dkis the envelope optical bandwidth and
qkis the FSR in wavelengths. The frequency response of the scheme was simulated for the Gaussian multimode laser and dispersive optical channel (25 km SSMF). The spectral pa-rameters of the laser are: center wavelength, k0 ¼ 1549 nm;
envelope spectral width, Dk ¼ 6 nm; FSR, dk ¼ 0.5 nm; mode FWHM,dk¼0.2 nm. Such parameters correspond to a real multimode laser.
The simulated laser spectrum is shown in Figure 2(a). To calculate the electrical frequency response, the laser light is externally modulated in a 0–20 GHz frequency range. Figure 2(b) shows the expected theoretical microwave response. The frequency response exhibits band-pass windows located at 0, 4.2, 8.4, 16.8,…GHz. In a practical approach, this frequency response can be used as band-pass microwave filters or for mul-tiplexing modulated microwave subcarriers that can be allocated in the transmission windows. This second approach is explored in the second part of this article.
Figure 1 Broad-band optical spectrum and dispersive-optical channel radio over fiber scheme
3. PHOTONIC FILTERING
The frequency response of the system described in the last sec-tion can be modified either by changing the length of the optical channel or by modifying the optical spectrum.
The first approach requires additional optical fiber lengths and is not considered in this study. The second approach is more attractive and very simple to implement, as the optical spectrum can be modified using fiber optic photonic filters. A photonic filter is modeled here as an optical retarder which introduces an optical delay or its equivalent OPD, Figure 3(a). An OPD can be easily implemented by birefringent polarization maintaining optical fibers (PMF) or birefringent electro-optic crystals. An OPD ‘‘channelizes’’ an optical spectrum and this effect has been described when studying coherence modulation of light [15, 16]. An optical retarder receives an optical signal s(t) and outputs s0ðtÞ ¼12sðtÞ þ12sðtsÞ, sis the optical delay.
In the Fourier domain, the energy spectral density at the output of the optical retarder corresponds to
S0ðkÞ ¼
1 2 S
ðkÞ þSðkÞexp j2p c k0 s
1
2 SðkÞ þSðkÞexp j2p c
k0s
This expression simplifies to the filtering function as
S0ðkÞ ¼
1
2PðkÞ 1þcosð 1
k0
2pdmÞ
(3)
where, P(k) is power spectrum of the optical source and dm ¼ csis the introduced OPD.
Figure 2 a) Multimode laser spectrum; b) Theoretical microwave frequency response
Calculations of different OPD’s for filtering the multimode laser were conducted. An optical regular filtering for the cancel-lation of one or more adjacent optical modes was searched. It was found that OPD’s of 2.2 and 1.48 mm matched for a peri-odic filtering of one and two alternate optical modes in order to increase FSR to 1 and 1.5 nm, respectively. The calculated fil-tering is depicted in Figure 3(b).
4. EXPERIMENTAL PHOTONIC FILTERING AND RECONFIGURATION OF THE FREQUENCY RESPONSE
The experimental setup for validating the selective optical filter-ing was based on the scheme of Figure 1, after insertfilter-ing the fiber photonic filter between the MMLD and an external wide-band LiNbO3 Mach-Zehnder electro-optic modulator. In such a
setup, a multimode laser emitting in the 1544–1554 nm wave-length range was used.
The optical filtering was achieved using fiber photonic filters, which were implemented by segments of PMF, as shown in Fig-ure 4. The PMF segments were placed between 45fiber polar-izers, to introduce OPDs, whose values were proportional to the fiber birefringence and length. From the simulation results, two segments of PMF for introducing OPD’s of 1.48 and 2.2 mm were realized. In Figure 5(a), the unfiltered optical spectrum is shown on the upper graph. The laser exhibits around 18 emis-sion modes with a FSR of 0.5 nm and spectral width of 0.1 nm. In this figure, the experimentally filtered spectra are also shown. The middle graph corresponds to the filtering by an OPD of 2.2 mm; the lower graph corresponds to the filtering by an OPD of 1.48 mm. The measured filtered spectra show excellent agree-ment to the calculated values from Eq. (3). As can be observed from Figure 5(a), the optical filtering modifies the spectrum increasing the FSRs from 0.5 nm to 1 and 1.5 nm.
After Eq. (1), the modified optical spectra will also modify the microwave frequency response of the dispersive-channel ra-dio over fiber scheme. According to the theoretical model, the new spectra will reconfigure the microwave frequency response and the periodic band-pass windows will be now centered at 2.1n and 1.05n GHz, respectively. The microwave frequency responses are shown in Figure 5(b). The upper curve corre-sponds to the unfiltered spectrum and shows the original micro-wave response, where the band-pass windows are centered at 4.2nGHz. The middle curve shows the frequency response for an OPD of 2.2 mm. This frequency response shows new bands Figure 4 A fiber optics photonic filter
Figure 5 Experimental optical filtering and the corresponding frequency responses: upper graphs, no optical filtering; middle graphs, optical filtering of 2.2 mm; lower graphs, optical filtering of 1.48 mm. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com]
centered at 2.1n GHz. The lower graph in Figure 5(b) corre-sponds to the frequency response for an OPD of 1.48 mm. In this last case, the frequency response shows microwave bands centered at 1.05nGHz. Such responses are in good agreement to the theoretical model.
5. EXPERIMENTAL MULTIPLEXED TRANSMISSION USING MICROWAVE SUBCARRIERS IN ADJACENT BAND-PASS WINDOWS
To show potential applications of the multilongitudinal source-dispersive channel scheme in the field of radio over fiber tele-communications, work has been conducted to show the trans-mission of multiplexed digital data-modulated microwave sub-carriers, which were allocated at adjacent transmission windows
around 7 and 8 GHz. Such bands were generated when the laser spectrum was filtered by an OPD of 1.48 mm [lower graph in Fig. 5(b)]. The experimental multiplexing transmission scheme is depicted in Figure 6. This scheme has been implemented using the multimode laser, a photonic filter introducing an OPD of 1.48 mm, a 20 GHz Mach-Zehnder electro-optic modulator, 25.2 km optical fiber channel, a 25 GHz photoreceiver, and home-designed microwave electronics (amplifiers, oscillators, mixers, etc). To test the multiplexed optical transmission, data streams of 34 Mbps, 223-1 NRZ and RZ formats were used to modulate the 6.8 and 8.25 GHz microwave subcarriers. The modulated subcarriers were transmitted through the optical chan-nel. At the receiver, the multiplexed microwave subcarriers were recuperated at the output of a low-noise amplifier stage. The Figure 6 Experimental setup for transmitting multiplexed modulated microwave subcarriers in band-pass windows. Inset (a), multiplexed data-modulated microwave subcarriers at 6.8 and 8.25 GHz
Figure 7 34 Mbps data-modulated subcarrier at 8.25 GHz: a) NRZ and RZ data formats; b) NRZ and RZ data spectrum after synchronous homodyne detection
received signals are naturally filtered by the transmission scheme and no electronic filters were used. Inset (a) in Figure 6, illustrates the multiplexed 6.8 and 8.25 GHz subcarriers. The system filtering effect is observed as the modulated spectra are confined around the center microwave frequencies. The laser noise level is at least 20 dB below the 6.8 GHz subcarrier level. As the 8.25 GHz subcarrier is the strongest signal, it has been chosen for demodulation to base-band by homodyne mix-ing, Figure 7. The graphs show the main lobes of the data sig-nals, which can be recuperated by further signal processing. The optical link introduced an attenuation equivalent to 30 dB. The received optical signal was amplified and compared to the elec-trical microwave subcarrier after this one was attenuated by 30 dB. This comparison is illustrated in Figure 7(a), where both electrical and optical signals show the same spectral distribution. To recuperate the base-band digital data, the 8.25 GHz subcar-rier was detected by synchronous homodyne mixing. In this stage, the received 8.25 GHz data-modulated subcarrier was mixed with an 8.25 GHz signal from a local oscillator. The resulting signal is the 34 Mbps base-band data stream, as depicted in Figure 7(b). The base-band signal was not further processed as this aspect was beyond the scope of this article. Work is in progress for integrating a complete data receiver [by adding the dashed line blocks in Fig. 7(b)], to evaluate the sys-tem performance, including parameters such as SNR, the BER, the dispersion power penalty, and so forth.
6. CONCLUSIONS
In the work, we have described the reconfiguration of the band pass transmission windows in the frequency response of an opti-cal transmission system using a multilongitudinal laser and a dis-persive optical channel. The introduction of optical delays can fil-ter the optical spectrum in a way to increase the optical FSR. The optical delays must be matched to the spectrum characteristics to achieve the filtering effect. The number of band-pass windows on an experimental setup has been increased, as has been demon-strated in this work, when using OPDs of 2.2 and 1.48 mm.
The introduced OPD’s have allowed a periodic filtering, eliminating alternate longitudinal modes. Such an effect intro-duced new band-pass windows in the resulting electrical micro-wave response of the studied scheme. The multiple band pass transmission windows, as described in this article, can be used for microwave filtering or multiplexing information on radio over fiber telecommunications schemes. Such capability has been successfully demonstrated by the simultaneous transmis-sion of digital signals using microwave carriers located in two adjacent transmission windows. The proposed scheme would be able to transmit several information signals using the low-pass frequency band and either digital or analog modulated micro-wave carriers, using the band-pass windows.
ACKNOWLEDGMENTS
This work was supported by a grant from the Mexican Consejo Nacional de Ciencia y Tecnologı´a (PY CONACYT 52148) and also by a technical collaboration between INAOE and Photline Technologies (PT). PT has provided samples of high speed electro-optic modulators for conducting electro-optical telecommunications research at INAOE.
REFERENCES
1. J. Martı´, F. Ramos, and R.I. Laming, Photonic microwave filter employing multimode optical sources and wideband chirped fibre gratings, Electron Lett 34 (1998), 1760–1761.
2. J. Campany, D. Pastor, and B. Ortega, Fibre optic microwave and millimetre-wave filter with high density sampling and very high sidelobe suppression using subnanometre optical spectrum slicing, Electron Lett 35 (1999), 494–496.
3. G. Yu, W. Zhang, and J.A.R Williams, High-performance micro-wave transversal filter using fiber Bragg grating arrays, IEEE Pho-ton Technol Lett 12 (2000), 1183–1185.
4. X. Yu, X. Zhang, H. Chi, and K. Chen, Photonic microwave trans-versal filter employing a fiber-Bragg-grating-based multiple resona-tor, Microwave Opt Technol Lett 40 (2005), 369–371.
5. J. Lue, H. Chi, X. Zhang, and L. Shen, Noise reduction using pho-tonic microwave filter for radio over fiber system, Microwave Opt Technol Lett 48 (2006), 305–307.
6. C. Gutierrez-Martinez, P. Mollier, H. Porte, L. Carca~no-Rivera, and J.P. Goedgebuer, Multichannel long-distance optical fiber transmission using dispersion-induced microwave transmission win-dows, Microwave Opt Technol Lett 36 (2003), 202–206.
7. C. Gutierrez-Martı´nez, J. Santos-Aguilar, J.A. Torres-Fortiz, and A. Morales-Dı´az. Reconfiguring dispersion-induced microwave trans-mission windows on radio over fiber schemes by using optical delays, In: Dig. 2007 IEEE International Topical Meeting on Microwave Photonics, 2007, pp.130–133.
8. D. Norton, S. Johns, C. Keefer, and R. Soref, Tunable microwave filtering using high dispersion fiber time delays, IEEE Photon Technol Lett 6 (1994), 831–832.
9. F. Coppinger, S. Yegnanarayanan, P.D. Trinh, B. Jalali, and I.L. Newberg, Nonrecursive tunable photonic filter using wavelenth-selective true time delay, IEEE Photon Technol Lett 8 (1996), 1214–1216.
10. D.B. Hunter and R Minasian, Tunable microwave fiber-optic band-pass filters, IEEE Photon Technol Lett 11 (1999), 874–876. 11. H. Chi and X. Zhang, A novel tunable fiber-optic microwave notch
filter using fiber loop and cascaded fiber Bragg gratings, Micro-wave Opt Technol Lett 41 (2004), 386–388.
12. K.-H. Lee, W.-Y. Choi, S. Choi, and K. Oh, A novel tunable fiber-optic microwave filtering using multimode DCF, IEEE Photon Technol Lett 15 (2003), 969–971.
13. H. Gouraud, P. di Bin, L. Billonet, B. Jarry, E. Lecroizier, M. Barge, and J.-L. Bougrenet, Reconfigurable and tunable micro-wave-photonics band-pass slicing filter using a dynamic gain equal-izer, Microwave Opt Technol Lett 48 (2006), 562–567.
14. D. Pastor, J. Campany, S. Sales, P. Mu~noz, and B. Ortega, Recon-figurable fiber-optic-based RF filters using current injection in mul-timode lasers, IEEE Photon Technol Lett 13 (2001), 1224–1226. 15. H. Porte, J.-P. Goedgebuer, and R. Ferriere, An LiNbO3 integrated
optics coherence modulator, J Lightwave Technol 10 (1992), 760–766. 16. C. Gutierrez-Martı´nez, B. Sanchez-Rinza, J. Rodrı´guez-Asomoza, and J. Pedraza-Contreras, Automated measurement of optical co-herence lengths and optical delays for applications in coco-herence- coherence-modulated optical transmissions, IEEE Trans Instrum Meas 49 (2000), 32–36.
VC2012 Wiley Periodicals, Inc.
IMPROVED MODEL OF
PSEUDOPOTENTIALS FOR ARRAY
ELEMENTS
Ioannis Psarros,1Vassiliki Kollia,2and George Fikioris1 1School of Electrical and Computer Engineering, National Technical University of Athens, Greece, GR 15-73 Zografou, Athens, Greece; Corresponding author: [email protected] 2
Hellenic Air Force Base, Larisa Base, GR 157-73 Larisa, Greece
Received 12 October 2011
ABSTRACT:A recent article has proposed a simplified model, based on the quantum-mechanical concept of the pseudopotential, for certain types of array elements, particularly for short linear dipoles. A
